So, a subtotal of $18.29 would end up costing $18.29 * 1.1025 = $20.1647, which would get rounded down to $20.16, right? A subtotal of $18.30 would end up costing $18.30 * 1.1025 = $20.1757, which would get rounded up to $20.18, right?

Is this correct, given Chicago's sales tax? If it is, what would be a loophole for getting a receipt totaling $20.17?

Changing the city/state doesn't change the nature of the question. Else we'd have the potential for at least 50 variants of this one.
– JoeTaxpayer♦Jan 13 '17 at 22:06

@JoeTaxpayer I understand that they are similar questions, but that question doesn't answer this one at all. In addition, this one has unique answers that don't answer the other question. They are not duplicates.
– Ben MillerJan 14 '17 at 2:11

Can you give me a hint why you feel these are different?
– JoeTaxpayer♦Jan 14 '17 at 2:14

@JoeTaxpayer Yes. The last sentence makes this question different. OP is trying to get a receipt to equal a specific amount, which, as we've seen from the answers, is more complex than a simple percent sales tax. (Gas tax, different rates for different items, etc.)
– Ben MillerJan 14 '17 at 2:20

Not quite seeing it, but you can have it.
– JoeTaxpayer♦Jan 14 '17 at 2:27

5 Answers
5

Gasoline is sold with the tax included in the price, which means it would be very easy to buy an exact dollar-and-cent amount of gas.
– Ben MillerJan 14 '17 at 4:57

@BenMiller - Isn't this the ideal answer? The fact that the gas meter is showing a built-in tax, you go to the register, hand the guy $20.17 and get your gas and the 2017 receipt. All else (IMHO) is a side issue.
– JoeTaxpayer♦Jan 15 '17 at 14:48

@JoeTaxpayer Agreed. This is a great answer, and I've already upvoted it.
– Ben MillerJan 15 '17 at 17:36

According to Wikipedia, the Illinois state sales tax (which is one component of the Chicago rate) can be different on different types of goods (e.g., groceries vs prepared food). It is left as an exercise to the reader to determine whether some particular combination of goods could be purchased under different tax rates so that the total comes to $20.17.

Also, depending on the state, they may have or permit specific rules for rounding which are other than strictly mathematical, such as tax tables, which change at arbitrarily chosen pennies, not necessarily the mathematically correct ones. **

That may be to break this very logjam for shops which include the tax in the price to simplify bill handling for cashiers, such as movie theaters on popcorn and drinks, volunteer-run gift shops, etc.

**much the way the IRS tax tables follow the tax formula, but only in staircase fashion. So if you make $50049, your tax is [making it up] $4000, but if you make $50050, your tax is $4025. IRS arbitrarily chooses the step points.

As suggested in BrenBarn's answer, the sales tax on groceries in Chicago is only 2.25%. Therefore, if you purchase $19.73 worth of food at a grocery store, your total should end up at $20.17, if the store rounds to the nearest penny. If they always round up to the next penny, $19.72 in groceries should give you the total you are looking for.

Not sure about Illinois, but my understanding is that most states round up or down to the nearest penny. I know for sure that Wisconsin requires rounding to the nearest penny, even if it is down.
– Ben MillerJan 14 '17 at 4:54